measures of centrality

1. measures of centrality

2. Last lecture summary • Which graphs did we meet? • scatter plot (bodový graf) • bar chart (sloupcový graf) • histogram • pie chart (koláčový graf) • How do they work, what are their advantages and/or disadvantages?

3. Random noise

4. Histogram • Now I will collect heights of all of you in this room. • Use Interactive Histogram Applet: http://www.shodor.org/interactivate/activities/Histogram/ • interval, bin

5. Histogram – Body fat • In Interactive Histogram Applet – choose „Body fat % in 252 men“ dataset. • Find reasonable bin size • Answer following questions. No matter of bin size what is always true? • Most scores fall around 20%. • The shape is roughly symmetrical. • Most scores fall in the middle of distribution. • There are more scores between 15 and 25 than between 35 and 50. • There are more scores between 0 and 10 than between 18 and 24. • Relatively more men have a body fat above 35% or below 5%.

6. Histogram – Income distribution • United States Census Bureau – http://www.census.gov

7. Histogram – Income distribution • This is an example of a (positively) skewed distribution (zprava zešikmené rozdělení). • This distribution is not symmetrical. • Most incomes fall to the left of the distribution.

8. Bar chart and scatter plot • Which scatter plot corresponds to this bar chart?

9. Pie chart to histogram • Which histogram looks like it cames from the same data?

10. About statistics • Statistics – the science of collecting, organizing, summaryzing, analyzing, and interpreting data • Goal – use imperfect information (our data) to infer facts, make predictions, and make decisions • Descriptive statistic – summarising data with numbers or pictures • Inferential statistics – making conclusions or decisions based on data

11. Choosing a profession Chemistry Geography 50 000 – 60 000 40 000 – 55 000

12. Choosing a profession • We made an interval estimate. • But ideally we want one number that describes the entire dataset. This allows us to quickly summarize all our data.

13. Choosing a profession • The value at which frequency is highest. • The value where frequency is lowest. • Value in the middle. • Biggest value o x-axis. • Mean Geography Chemistry

14. Three big M’s • The value at which frequency is highest is called the mode. i.e. the most common value is the mode. • The value in the middle of the distribution is called the median. • The mean is the mean. Geography Chemistry

15. Quick quiz • What is the mode in our data?

16. Mode in negatively skewed distribution

17. Mode in uniform distribution

18. Multimodal distribution

19. Mode in categorical data

20. More of mode True or False? • The mode can be used to describe any type of data we have, whether it’s numerical or categorical. • All scores in the dataset affect the mode. • If we take a lot of samples from the same population, the mode will be the same in each sample. • There is an equation for the mode. • Ad 3. • http://onlinestatbook.com/stat_sim/sampling_dist/ • Mode changes as you change a bin size. • The mode depends on how you present data. And we can’t use mode to learn something about our population.

21. Life expectancy data • Watch TED talk by Hans Rosling, Gapminder Foundation: http://www.ted.com/talks/hans_rosling_shows_the_best_stats_you_ve_ever_seen.html